It’s a PHP question, and not related to WordPress, but I’m answering because you are messing with codes. Just make it easy, and you also can go through it. 🙂
<?php
/**
* get your custom field data and store into a variable
* to make it easy - nothing else
*/
$my_custom_field = get_post_meta( $post->ID, 'rtm_nights', $single=true );
if ( $my_custom_field == '3 nights' ) {
get_template_part( 'content', 'fourday' );
} else if ( $my_custom_field == '2 nights' ) {
get_template_part( 'content', 'threeday' );
} else if ( $my_custom_field == '1 night' ) {
get_template_part( 'content', 'twoday' );
} else if ( $my_custom_field == 'no nights') {
get_template_part( 'content', 'oneday' );
} //endif
?>
EDIT
And you are missing something about get_post_meta()
syntax:
<?php get_post_meta( $post_id, $key, $single ); ?>
Value cannot be checked through it. 🙂